Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-2449Articles in Press20231114$C^*$-algebra-valued $S_b$-metric spaces and applications to integral equations528210.22060/ajmc.2023.22211.1140ENSeyede SamiraRazaviFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran0000-0002-9772-1140HashemParvaneh MasihaFaculty of Mathematics, K. N. Toosi University of Technology, Tehran, IranJournal Article20230217We first introduce the concept of $C^*$-algebra-valued $S_{b}$-metric space, then we prove Banach contraction principle in this space. Finally, existence and uniqueness results for one type of integral equation is discussed.